Problem: Reduce to lowest terms: $- \dfrac{8}{7} \div - \dfrac{8}{3} = {?}$
Explanation: Dividing by a fraction is the same as multiplying by the reciprocal of the fraction. The reciprocal of $- \dfrac{8}{3}$ is $- \dfrac{3}{8}$ Therefore: $ - \dfrac{8}{7} \div - \dfrac{8}{3} = - \dfrac{8}{7} \times - \dfrac{3}{8} $ $ \phantom{- \dfrac{8}{7} \times - \dfrac{3}{8}} = \dfrac{-8 \times -3}{7 \times 8} $ $ \phantom{- \dfrac{8}{7} \times - \dfrac{3}{8}} = \dfrac{24}{56} $ The numerator and denominator have a common divisor of $8$, so we can simplify: $ \dfrac{24}{56} = \dfrac{24 \div 8}{56 \div 8} = \dfrac{3}{7} $